Remember that there are two quadrants where sin(x) = 0.34 (both first and second quadrant), so x may be either 19.88 degrees or 180 -19.88 = 160.12 degrees. And furher since the final answer must be in the range 0 < x < 360, that means that 5x/2+15 will be in the range 15 to 915 degrees. Which means in addition to 5x/2= 19.88 you also have 5x/2=19.88 + 360 and 5x/2+15 = 19.88+ 2x360 degrees. Same with 5x/2+15=160.12, 5x/2+15= 160.12+360, etc.
One other comment - no fault of yours given the answers in the form that that you were given, but it drives me crazy to see answers taken out to 10 decimal places of accuracy when the data you were given is only two decimal places. The proper answer for the first one is x=1.95, not x= 1.950749628.